In this subsection, we formulate a new IM problem under our setting assuming topologically unknown attributed networks with node features.
In a given diffusion model, we define a function \(I(S)\)  : \(2^{\mathcal {V}_T} \rightarrow [0, n]\)  that maps a seed set \(S\)  to the number of influenced nodes in the underlying graph \(G\)  at the end of the diffusion process, which is a random variable since the same set \(S\)  results in different network realizations.
In our study, based on the concept of active learning [1]}, [2]}, we aim to maximize the expected influence spread \(\sigma (S)=\operatorname{{E}}(I(S))\)  by jointly finding a sequence of queries \((v_0,v_1, \cdots ,v_{T-1})\)  that leads to the finally discovered subgraph \(G_T\) , as well as a seed set \(S \subseteq \mathcal {V}_T\) , given a query budget \(T\)  and a seed budget \(k\) . This is also referred to as an exploratory IM problem in the literature [3]}, [4]}.
In contrast to the conventional setting of IM [5]}, since the influence spread \(\sigma (\cdot )\)  cannot be computed accurately from \(G\)  due to the uncertainty of the unexplored part of \(G\) , our problem is ill-defined. Thus, we need to compute an estimate of \(\sigma (\cdot )\)  based on the available information.
